Problem stringlengths 5 967 | Rationale stringlengths 1 2.74k | options stringlengths 37 300 | correct stringclasses 5
values | annotated_formula stringlengths 7 6.48k | linear_formula stringlengths 8 925 | category stringclasses 6
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right triangle abc is the base of the prism in the figure above . if ab = ac = â ˆ š 10 and the height of the prism is 4 , what is the volume of the prism ? | "volume of prism = area of base * height = 1 / 2 * ( square root of 10 ) * ( square root of 10 ) * 4 = 20 answer : c" | a ) 40 , b ) 85 , c ) 20 , d ) 60 , e ) 45 | c | divide(volume_rectangular_prism(sqrt(10), sqrt(10), 4), 10) | sqrt(n0)|volume_rectangular_prism(n1,#0,#0)|divide(#1,n0)| | geometry |
a woman swims downstream 54 km and upstream 6 km taking 6 hours each time , what is the speed of the woman in still water ? | "54 - - - 6 ds = 9 ? - - - - 1 6 - - - - 6 us = 1 ? - - - - 1 m = ? m = ( 9 + 1 ) / 2 = 5 answer : d" | a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6 | d | divide(add(divide(54, 6), divide(6, 6)), const_2) | divide(n0,n2)|divide(n1,n2)|add(#0,#1)|divide(#2,const_2)| | physics |
what is the least number which when divided by 7 , 9 , 12 and 18 leaves remainder 4 in each care ? | "explanation : lcm of 7 , 9 , 12 and 18 is 252 required number = 252 + 4 = 256 answer : option d" | a ) 230 , b ) 240 , c ) 236 , d ) 256 , e ) 266 | d | add(lcm(lcm(7, 9), lcm(12, 18)), 4) | lcm(n0,n1)|lcm(n2,n3)|lcm(#0,#1)|add(n4,#2)| | general |
how many points ( x , y ) lie on the line segment between ( 15 , 12 2 / 3 ) and ( 7 , 17 2 / 3 ) such that x and y are both integers ? | slope = ( 17 2 / 3 - 12 2 / 3 ) / ( 7 - 15 ) = - 5 / 8 y = mx + b = > 12 2 / 3 = - 15 * 5 / 8 + b = > b = 1 y = - 75 x / 8 + 22 only integer values work , and the only multiples of 8 between 7 and 15 for x value is 8 , thus 1 point . a | a ) 1 , b ) 5 , c ) 7 , d ) 8 , e ) 9 | a | divide(7, 7) | divide(n4,n4) | general |
a statue is being carved by a sculptor . the original piece of marble weighed 250 kg . in the first week 30 per cent is cut away . in the second week 20 per cent of the remainder is cut away . in the third week the statue is completed when 25 percent of the remainder is cut away . what is the weight of the final statue... | "a 105 kg = 250 ã — 0.7 ã — 0.8 ã — 0.75 ." | a ) 105 kg , b ) 145 kg , c ) 165 kg , d ) 115 kg , e ) 100 kg | a | multiply(subtract(const_1, divide(25, const_100)), multiply(subtract(const_1, divide(20, const_100)), multiply(250, subtract(const_1, divide(30, const_100))))) | divide(n1,const_100)|divide(n2,const_100)|divide(n3,const_100)|subtract(const_1,#0)|subtract(const_1,#1)|subtract(const_1,#2)|multiply(n0,#3)|multiply(#6,#4)|multiply(#7,#5)| | gain |
a bowl was filled with 10 ounces of water , and 0.008 ounce of the water evaporated each day during a 50 - day period . what percent of the original amount of water evaporated during this period ? | "total amount of water evaporated each day during a 50 - day period = . 008 * 50 = . 008 * 100 / 2 = . 8 / 2 = . 4 percent of the original amount of water evaporated during this period = ( . 4 / 10 ) * 100 % = 4 % answer d" | a ) 0.004 % , b ) 0.04 % , c ) 0.40 % , d ) 4 % , e ) 40 % | d | multiply(divide(multiply(50, 0.008), 10), const_100) | multiply(n1,n2)|divide(#0,n0)|multiply(#1,const_100)| | gain |
a goods train runs at the speed of 72 km / hr and crosses a 260 m long platform in 26 sec . what is the length of the goods train ? | speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , ( x + 260 ) / 26 = 20 x = 260 m . answer : d | a ) 278 , b ) 166 , c ) 151 , d ) 260 , e ) 109 | d | subtract(multiply(multiply(divide(72, const_3600), const_1000), 26), 260) | divide(n0,const_3600)|multiply(#0,const_1000)|multiply(n2,#1)|subtract(#2,n1) | physics |
when positive integer n is divided by positive integer j , the remainder is 12 . if n / j = 134.08 , what is value of j ? | "1 ) we know that decimal part of decimal quotient = { remainder / divisor } so 0.08 , the decimal part of the decimal quotient , must equal the remainder , 12 , divided by the divisor j . 0.08 = 12 / j 0.08 * j = 12 j = 12 / 0.08 = 1200 / 8 = 300 / 2 = 150 so j = 150 , answer = e ." | a ) 22 , b ) 56 , c ) 78 , d ) 112 , e ) 150 | e | divide(12, subtract(134.08, add(const_100, add(multiply(const_4, const_10), const_2)))) | multiply(const_10,const_4)|add(#0,const_2)|add(#1,const_100)|subtract(n1,#2)|divide(n0,#3)| | general |
q is a set of 8 distinct prime numbers . if the sum of the integers in q is even and the number x is a member of q , then what is the least value that x can be ? | 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 = 77 ( discard as sum is odd ) 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 = 98 ( sum is even ) least number = 3 b | a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 7 | b | add(divide(8, const_4), const_1) | divide(n0,const_4)|add(#0,const_1) | general |
in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 58 liters and they are all empty , how much money total will it cost to fuel all cars ? | "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 58 ) = 473.40 hence answer will be ( e )" | a ) 320.40 $ , b ) 383.40 $ , c ) 420.40 $ , d ) 450.40 $ , e ) 473.40 $ | e | multiply(multiply(0.65, 58), 12) | multiply(n1,n3)|multiply(n2,#0)| | general |
in the xy - plane , a triangle has vertices ( 0,0 ) , ( 4,0 ) and ( 4,7 ) . if a point ( a , b ) is selected at random from the triangular region , what is the probability that a - b > 0 ? | "the area of the right triangle is ( 1 / 2 ) * 4 * 7 = 14 . only the points ( a , b ) below the line y = x satisfy a - b > 0 . the part of the triangle which is below the line y = x has an area of ( 1 / 2 ) ( 4 ) ( 4 ) = 8 . p ( a - b > 0 ) = 8 / 14 = 4 / 7 the answer is a ." | a ) 4 / 7 , b ) 2 / 3 , c ) 3 / 5 , d ) 3 / 7 , e ) 1 / 2 | a | divide(const_4, add(0,0, const_10)) | add(n0,const_10)|divide(const_4,#0)| | geometry |
( 565945 x 121 ) = ? | 565945 * 121 = 68479345 ans c | a ) 68463812 , b ) 68463813 , c ) 68479345 , d ) 68463814 , e ) 68463814 | c | multiply(565945, power(add(const_4, const_1), const_4)) | add(const_1,const_4)|power(#0,const_4)|multiply(n0,#1)| | general |
mixture a is 20 percent alcohol , and mixture b is 50 percent alcohol . if the two are poured together to create a 15 gallon mixture that contains 30 percent alcohol , approximately how many gallons of mixture a are in the mixture ? | let a = number of gallons on mixture a in 15 gallon mixture b = number of gallons on mixture b in 15 gallon mixture ( 20 / 100 ) a + ( 50 / 100 ) b = ( 30 / 100 ) ( a + b ) - - 1 a + b = 15 - - 2 on solving equations 1 and 2 , we get a = 10 b = 5 answer d 10 gallons | a ) 3 gallons , b ) 4 gallons , c ) 5 gallons , d ) 10 gallons , e ) 12 gallons | d | divide(divide(multiply(20, 50), 50), const_2) | multiply(n0,n1)|divide(#0,n1)|divide(#1,const_2) | gain |
sum of two numbers prime to each other is 14 and their l . c . m . is 45 . what are the numbers ? | "as two numbers are prime , satisfies all but option c will make the product of numbers i . e 45 answer : c" | a ) 6 and 5 , b ) 8 and 5 , c ) 9 and 5 , d ) 8 and 5 , e ) 3 and 5 | c | add(45, 14) | add(n0,n1)| | physics |
if 5 is one solution of the equation x ^ 2 + 3 x + k = 10 , where k is a constant , what is the other solution ? | "the phrase “ 5 is one solution of the equation ” means that one value of x is 5 . thus , we first must plug 5 for x into the given equation to determine the value of k . so we have 5 ^ 2 + ( 3 ) ( 5 ) + k = 10 25 + 15 + k = 10 40 + k = 10 k = - 30 next we plug - 30 into the given equation for k and then solve for x . ... | a ) - 8 , b ) - 4 , c ) - 3 , d ) 1 , e ) 6 | a | divide(subtract(10, add(power(5, 2), multiply(3, 5))), 5) | multiply(n0,n2)|power(n0,n1)|add(#0,#1)|subtract(n3,#2)|divide(#3,n0)| | general |
if 350 ! / 10 ^ n is an integer , what is the largest possible value of n ? | "the question actually asks the highest power of 10 which divides 350 ! ( for a number to be an integer - without any remainder all the trailing zeroe ' s must be divided by the denominator ) 10 = 2 x 5 350 factorial will have 86 as - 350 / 5 = 70 70 / 5 = 14 14 / 5 = 2 so answer will be ( c ) 86" | a ) 88 , b ) 82 , c ) 86 , d ) 87 , e ) 80 | c | add(divide(divide(350, add(const_4, const_1)), add(const_4, const_1)), divide(350, add(const_4, const_1))) | add(const_1,const_4)|divide(n0,#0)|divide(#1,#0)|add(#2,#1)| | general |
a person decided to build a house in 100 days . he employed 100 men in the beginning and 100 more after 80 days and completed the construction in stipulated time . if he had not employed the additional men , how many days behind schedule would it have been finished ? | "200 men do the rest of the work in 100 - 80 = 20 days 100 men can do the rest of the work in 20 * 200 / 100 = 40 days required number of days = 40 - 80 = 40 days answer is a" | a ) 40 , b ) 80 , c ) 70 , d ) 60 , e ) 50 | a | subtract(100, 80) | subtract(n0,n3)| | general |
solve the quickfire maths brain teaser â ˆ š 4 % = ? | â ˆ š 4 % = > â ˆ š 4 / â ˆ š 100 = > 2 / 10 = > 20 / 100 = > 20 % e | a ) 30 % , b ) 40 % , c ) 85 % , d ) 19 % , e ) 20 % | e | divide(const_100, add(const_1, 4)) | add(n0,const_1)|divide(const_100,#0) | gain |
the area of sector of a circle whose radius is 12 metre and whose angle at the center is 42 ° is ? | 42 / 360 * 22 / 7 * 12 * 12 = 52.8 m 2 answer : c | a ) 52.7 m 2 , b ) 57.8 m 2 , c ) 52.8 metre sq , d ) 72.8 m 2 , e ) 52.8 m 2 | c | multiply(multiply(power(12, const_2), divide(add(multiply(const_2, const_10), const_2), add(const_4, const_3))), divide(42, divide(const_3600, const_10))) | add(const_3,const_4)|divide(const_3600,const_10)|multiply(const_10,const_2)|power(n0,const_2)|add(#2,const_2)|divide(n1,#1)|divide(#4,#0)|multiply(#6,#3)|multiply(#5,#7) | physics |
in a race of 1000 meters , a can beat b by 100 meters , in a race of 800 meters , b can beat c by 100 meters . by how many meters will a beat c in a race of 600 meters ? | explanation : when a runs 1000 meters , b runs 900 meters and when b runs 800 meters , c runs 700 meters . therefore , when b runs 900 meters , the distance that c runs = ( 900 x 700 ) / 800 = 6300 / 8 = 787.5 meters . so , in a race of 1000 meters , a beats c by ( 1000 - 787.5 ) = 212.5 meters to c . so , in a race of... | a ) 125.5 meters , b ) 126.5 meters , c ) 127.5 meters , d ) 128.5 meters , e ) none of these | c | divide(multiply(600, subtract(1000, divide(multiply(subtract(1000, 100), subtract(800, 100)), 800))), 1000) | subtract(n0,n1)|subtract(n2,n1)|multiply(#0,#1)|divide(#2,n2)|subtract(n0,#3)|multiply(n4,#4)|divide(#5,n0) | physics |
if a and b get profits of rs . 18,000 and rs . 15,000 respectively at the end of year then ratio of their investments are | "ratio = 18000 / 15000 = 6 : 5 answer : a" | a ) 6 : 5 , b ) 1 : 4 , c ) 3 : 2 , d ) 2 : 3 , e ) 2 : 5 | a | divide(multiply(multiply(multiply(const_3, const_2), const_100), const_100), divide(multiply(multiply(multiply(const_3, const_2), const_100), const_100), multiply(add(const_2, const_3), const_2))) | add(const_2,const_3)|multiply(const_2,const_3)|multiply(#1,const_100)|multiply(#0,const_2)|multiply(#2,const_100)|divide(#4,#3)|divide(#4,#5)| | gain |
he ratio between the sale price and the cost price of an article is 5 : 3 . what is the ratio between the profit and the cost price of that article ? | let c . p . = rs . 3 x and s . p . = rs . 5 x . then , gain = rs . 2 x required ratio = 5 x : 2 x = 5 : 2 answer : d | a ) 2 : 6 , b ) 2 : 9 , c ) 2 : 4 , d ) 5 : 2 , e ) 2 : 5 | d | inverse(subtract(const_1, divide(3, 5))) | divide(n1,n0)|subtract(const_1,#0)|inverse(#1) | other |
the average of 6 observations is 12 . a new observation is included and the new average is decreased by 1 . the seventh observation is ? | "let seventh observation = x . then , according to the question we have = > ( 72 + x ) / 7 = 11 = > x = 5 . hence , the seventh observation is 5 . answer : c" | a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 7 | c | subtract(multiply(subtract(12, 1), add(6, 1)), multiply(12, 6)) | add(n0,n2)|multiply(n0,n1)|subtract(n1,n2)|multiply(#0,#2)|subtract(#3,#1)| | general |
a certain bag contains 100 balls â € ” 50 white , 20 green , 10 yellow , 17 red , and 3 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ? | "according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 50 + 20 + 10 ) / 100 = 80 / 100 = 0.8 . answer is d" | a ) 0.9 , b ) 0.75 , c ) 0.6 , d ) 0.8 , e ) 0.5 | d | divide(subtract(100, add(17, 3)), 100) | add(n4,n5)|subtract(n0,#0)|divide(#1,n0)| | other |
simplify : 8888 + 888 + 88 + 8 | "8888 888 88 8 - - - - - - - 9872 answer is a ." | a ) 9872 , b ) 9782 , c ) 9827 , d ) 9287 , e ) none of them | a | add(multiply(8888, 888), multiply(88, 8)) | multiply(n0,n1)|multiply(n2,n3)|add(#0,#1)| | general |
for an agricultural experiment , 300 seeds were planted in one plot and 200 were planted in a second plot . if exactly 15 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated ? | "in the first plot 15 % of 300 seeds germinated , so 0.15 x 300 = 45 seeds germinated . in the second plot , 35 % of 200 seeds germinated , so 0.35 x 200 = 70 seeds germinated . since 45 + 70 = 115 seeds germinated out of a total of 300 + 200 = 500 seeds , the percent of seeds that germinated is ( 115 / 500 ) x 100 % ,... | a ) 12 % , b ) 26 % , c ) 23 % , d ) 30 % , e ) 60 % | c | multiply(divide(add(multiply(divide(15, const_100), 300), multiply(divide(35, const_100), 200)), add(300, 200)), const_100) | add(n0,n1)|divide(n2,const_100)|divide(n3,const_100)|multiply(n0,#1)|multiply(n1,#2)|add(#3,#4)|divide(#5,#0)|multiply(#6,const_100)| | general |
a man sitting in a train which is travelling at 50 kmph observes that a goods train , travelling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed . | "relative speed = ( 280 ⁄ 9 ) m / sec = ( 280 ⁄ 9 × 18 ⁄ 5 ) kmph = 112 kmph . ∴ speed of goods train = ( 112 – 50 ) kmph = 62 kmph . answer a" | a ) 62 kmph , b ) 58 kmph , c ) 52 kmph , d ) 50 kmph , e ) none of these | a | subtract(multiply(divide(280, 9), const_3_6), 50) | divide(n2,n1)|multiply(#0,const_3_6)|subtract(#1,n0)| | physics |
a can do a work in 15 days and b in 20 days . if they work on it together then in how many days required to complete the work ? | person ( a ) ( b ) ( a + b ) time - ( 15 ) ( 20 ) ( 300 / 35 ) rate - ( 20 ) ( 15 ) ( 35 ) work - ( 300 ) ( 300 ) ( 300 ) therefore a + b requires ( 300 / 35 ) days to complete entire work = 300 / 35 answer is b | a ) 300 / 31 , b ) 300 / 35 , c ) 300 / 21 , d ) 300 / 15 , e ) 300 / 20 | b | inverse(add(divide(const_1, 15), divide(const_1, 20))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|inverse(#2) | physics |
what is the average of 1200 , 1300 , 1400 , 1510 , 1520 , 1530 , 1115 , 1120 , and 1125 ? | "add 1200 , 1300 , 1400 , 1510 , 1520 , 1530 , 1115 , 1120 , and 1125 grouping numbers together may quicken the addition sum = 11820 11820 / 9 = 1313.33 c" | a ) 1345 , b ) 1334 , c ) 1313.33 , d ) 1350 , e ) 1325 | c | divide(add(add(add(add(add(add(1200, 1300), 1400), 1510), 1520), 1530), 1200), add(const_3, const_4)) | add(n0,n1)|add(const_3,const_4)|add(n2,#0)|add(n3,#2)|add(n4,#3)|add(n5,#4)|add(n0,#5)|divide(#6,#1)| | general |
the speed of a car is 90 km in the first hour and 50 km in the second hour . what is the average speed of the car ? | "s = ( 90 + 50 ) / 2 = 70 kmph answer : a" | a ) 70 , b ) 75 , c ) 88 , d ) 54 , e ) 15 | a | divide(add(90, 50), const_2) | add(n0,n1)|divide(#0,const_2)| | physics |
of the 200 employees in a certain company , 25 percent will be relocated to city x and the remaining 75 percent will be relocated to city y . however , 45 percent of the employees prefer city y and 55 percent prefer city x . what is the highest possible number of employees who will be relocated to the city they prefer ... | "110 prefer x ( group 1 ) ; 90 prefer y ( group 2 ) . city y needs 150 people : letall 90 who prefer y ( entire group 2 ) be relocated there , the rest 60 will be those who prefer x from group 1 ; city x needs 40 people : 110 - 60 = 40 from group 1 will be relocated to x , which they prefer . so , the highest possible ... | a ) 65 , b ) 100 , c ) 115 , d ) 130 , e ) 135 | d | add(multiply(45, const_2), 55) | multiply(n3,const_2)|add(n4,#0)| | gain |
a starts business with rs . 3500 and after 9 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b â € ™ s contribution in the capital ? | "explanation : a invested rs . 3500 for 12 months . let b joined with investment x . and he invested for 12 - 9 = 3 months . so there profit ratio = ( 3500 ã — 12 ) : ( 3 x ) = 2 : 3 â ‡ ’ x = 21000 answer : d" | a ) 24887 , b ) 20778 , c ) 23788 , d ) 21000 , e ) 2811 | d | divide(multiply(multiply(3500, const_12), 3), multiply(subtract(const_12, 9), 2)) | multiply(n0,const_12)|subtract(const_12,n1)|multiply(n3,#0)|multiply(n2,#1)|divide(#2,#3)| | other |
a shirt goes on sale for 80 % of its original price . one week later , the sale price is marked down 10 % . the final price is what percent of the original price ? | "just assume original price is 100 . sale price = 80 then it is marked down by 10 % = 80 - 8 = 72 . hence it is 72 % of the original price . hence answer is a" | a ) 72 % , b ) 70 % , c ) 52 % , d ) 50 % , e ) 28 % | a | subtract(80, multiply(divide(80, const_100), 10)) | divide(n0,const_100)|multiply(n1,#0)|subtract(n0,#1)| | gain |
what is the sum of all the prime factors of 220 and 330 ? | "prime factorization of both the numbers is as follows 220 = 2 * 2 * 5 * 11 sum of the prime factors of 220 = 20 330 = 2 * 3 * 5 * 11 sum of prime factors of 330 = 21 addition of both = 20 + 21 = 41 answer d" | a ) 15 , b ) 21 , c ) 35 , d ) 41 , e ) 64 | d | multiply(add(divide(subtract(subtract(330, 220), const_2), const_2), 220), divide(add(subtract(330, 220), const_2), const_2)) | subtract(n1,n0)|add(#0,const_2)|subtract(#0,const_2)|divide(#2,const_2)|divide(#1,const_2)|add(n0,#3)|multiply(#5,#4)| | other |
mr . evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children . if mr . evans has 5 children and 6 grandchildren , then approximately what percentage of mr . evans estat... | "share of each child ( 5 no ) and ( total share of grand children together ) 1 no = 1 / ( 5 + 1 ) = 1 / 6 as the grand children again equally share the part given to them : share of each grand child = [ ( 1 / 6 ) / 6 ] = 1 / 36 = 2.8 % answer : e" | a ) 20 % , b ) 17 % , c ) 4.0 % , d ) 3.3 % , e ) 2.8 % | e | multiply(divide(divide(divide(const_100, const_3), 6), const_100), const_100) | divide(const_100,const_3)|divide(#0,n1)|divide(#1,const_100)|multiply(#2,const_100)| | general |
how many numbers from 10 to 50 are exactly divisible by 3 | "12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 , 42 , 45,48 . 13 numbers . 10 / 3 = 3 and 50 / 3 = 16 = = > 16 - 3 = 13 . therefore 13 digits b )" | a ) 11 , b ) 13 , c ) 15 , d ) 18 , e ) 19 | b | add(divide(subtract(multiply(floor(divide(50, 3)), 3), multiply(add(floor(divide(10, 3)), const_1), 3)), 3), const_1) | divide(n1,n2)|divide(n0,n2)|floor(#0)|floor(#1)|add(#3,const_1)|multiply(n2,#2)|multiply(n2,#4)|subtract(#5,#6)|divide(#7,n2)|add(#8,const_1)| | general |
at what rate of compound interest per annum will a sum of rs . 1200 become rs . 1348.32 in 2 years | "explanation : let rate will be r % 1200 ( 1 + r / 100 ) 2 = 134832 / 100 ( 1 + r / 100 ) 2 = 134832 / 120000 ( 1 + r / 100 ) 2 = 11236 / 10000 ( 1 + r / 100 ) = 106 / 100 = > r = 6 % option d" | a ) 3 % , b ) 4 % , c ) 5 % , d ) 6 % , e ) 7 % | d | subtract(sqrt(divide(multiply(1348.32, const_100), divide(1200, const_100))), sqrt(divide(multiply(1200, const_100), divide(1200, const_100)))) | divide(n0,const_100)|multiply(n1,const_100)|multiply(n0,const_100)|divide(#1,#0)|divide(#2,#0)|sqrt(#3)|sqrt(#4)|subtract(#5,#6)| | gain |
a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 30 paisa . if the share of y is rs . 18 , what is the total amount ? | "x : y : z = 100 : 45 : 30 20 : 9 : 6 9 - - - 18 35 - - - ? = > 70 answer : a" | a ) 70 , b ) 105 , c ) 178 , d ) 177 , e ) 169 | a | add(add(multiply(divide(const_100, 45), 18), multiply(divide(30, 45), 18)), 18) | divide(const_100,n0)|divide(n1,n0)|multiply(n2,#0)|multiply(n2,#1)|add(#2,#3)|add(n2,#4)| | general |
andrew purchased 7 kg of grapes at the rate of 68 per kg and 9 kg of mangoes at the rate of 48 per kg . how much amount did he pay to the shopkeeper ? | "cost of 7 kg grapes = 68 × 7 = 476 . cost of 9 kg of mangoes = 48 × 9 = 432 . total cost he has to pay = 476 + 432 = 908 b" | a ) 1000 , b ) 908 , c ) 930 , d ) 1075 , e ) 1080 | b | add(multiply(7, 68), multiply(9, 48)) | multiply(n0,n1)|multiply(n2,n3)|add(#0,#1)| | gain |
two numbers a and b are such that the sum of 5 % of a and 3 % of b is two - third of the sum of 6 % of a and 8 % of b . find the ratio of a : b . | "explanation : 5 % of a + 3 % of b = 2 / 3 ( 6 % of a + 8 % of b ) 5 a / 100 + 3 b / 100 = 2 / 3 ( 6 a / 100 + 8 b / 100 ) ⇒ 5 a + 3 b = 2 / 3 ( 6 a + 8 b ) ⇒ 15 a + 9 b = 12 a + 16 b ⇒ 3 a = 7 b ⇒ ab = 7 / 3 ⇒ a : b = 7 : 3 answer : option c" | a ) 2 : 1 , b ) 1 : 2 , c ) 7 : 3 , d ) 1 : 1 , e ) 3 : 2 | c | divide(subtract(divide(multiply(divide(8, const_100), 3), const_3), divide(3, const_100)), subtract(divide(5, const_100), divide(multiply(divide(6, const_100), const_2), const_3))) | divide(n3,const_100)|divide(n1,const_100)|divide(n0,const_100)|divide(n2,const_100)|multiply(#0,n1)|multiply(#3,const_2)|divide(#4,const_3)|divide(#5,const_3)|subtract(#6,#1)|subtract(#2,#7)|divide(#8,#9)| | general |
radha bought a watch for rs . 144 and got a percentage of profit equal to the cost price of the watch . what is the cost price of the watch ? | sp = 144 cp = x profit % = x c . p . = ( 100 / ( 100 + gain % ) ) * s . p . x = ( 100 / 100 + x ) * 144 x ^ 2 + 100 x = 14400 x ^ 2 + 180 x - 80 x - 14400 = 0 ( x + 180 ) ( x - 80 ) = 0 x = - 180 x = 80 answer : d | a ) rs . 72 , b ) rs . 78 , c ) rs . 80 , d ) rs . 90 , e ) rs . 92 | d | add(divide(subtract(sqrt(add(multiply(const_100, const_100), multiply(multiply(const_100, 144), const_4))), const_100), const_2), const_10) | multiply(const_100,const_100)|multiply(n0,const_100)|multiply(#1,const_4)|add(#0,#2)|sqrt(#3)|subtract(#4,const_100)|divide(#5,const_2)|add(#6,const_10) | gain |
a and b are two partially filled buckets of water . if 3 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 3 liters are transferred from b to a , b would contain one - half of the amount of water in a . bucket a contains how many liters of water ? | "let bucket a be a and bucket b be b scenario 1 a - 3 = 1 / 3 ( b + 3 ) - - - - > 3 a - 9 = b + 3 scenario 2 b - 3 = 1 / 2 ( a + 3 ) - - - - - > 2 b - 6 = a + 3 from scenario 1 , b = 3 a - 12 substitute b with this information in stmt 2 2 ( 3 a - 12 ) - 9 = a + 3 - - - - - - > 6 a - 24 - 9 = a + 3 - - - - - - > 6 a - a... | a ) 36 / 5 , b ) 13 , c ) 17 , d ) 21 , e ) 23 | a | divide(multiply(add(add(3, const_3), const_2), divide(3, const_2)), add(const_2, divide(const_1, const_2))) | add(n0,const_3)|divide(n0,const_2)|divide(const_1,const_2)|add(#0,const_2)|add(#2,const_2)|multiply(#3,#1)|divide(#5,#4)| | general |
27 is a perfect cube . when x is perfect cube which is added to the prime factor of 27 , the result is not a prime number . what is the square root of x ? | 27 is 3 * 3 * 3 2 * 2 = 4 , 3 + 4 = 7 4 * 4 = 16 , 3 + 16 = 17 6 * 6 = 36 , 3 + 36 = 39 8 * 8 = 64 , 3 + 64 = 67 10 * 10 = 100 , 3 + 100 = 103 here c is the only addition that is not a prime number . so the answer is c | ['a ) 2', 'b ) 4', 'c ) 6', 'd ) 8', 'e ) 10'] | c | sqrt(add(27, multiply(const_2, multiply(const_2, const_2)))) | multiply(const_2,const_2)|multiply(#0,const_2)|add(n0,#1)|sqrt(#2) | other |
| x + 3 | – | 4 - x | = | 8 + x | how many k solutions will this equation have ? | "| x | = x when x > = 0 ( x is either positive or 0 ) | x | = - x when x < 0 ( note here that you can put the equal to sign here as well x < = 0 because if x = 0 , | 0 | = 0 = - 0 ( all are the same ) so the ' = ' sign can be put with x > 0 or with x < 0 . we usually put it with ' x > 0 ' for consistency . a" | a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | a | divide(multiply(add(4, 3), const_2), 8) | add(n0,n1)|multiply(#0,const_2)|divide(#1,n2)| | general |
the units digit of ( 35 ) ^ ( 87 ) + ( 93 ) ^ ( 55 ) is : | "the units digit of powers of 3 , cycles in a group of 4 : { 3 , 9 , 7 , 1 } 55 has the form 4 k + 3 , so the units digit of 93 ^ 55 is 7 . the units digit of powers of 5 is always 5 . 7 + 5 = 12 , so the units digit is 2 . the answer is a ." | a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0 | a | add(reminder(multiply(reminder(55, const_4), 93), const_10), reminder(35, const_10)) | reminder(n3,const_4)|reminder(n0,const_10)|multiply(n2,#0)|reminder(#2,const_10)|add(#3,#1)| | general |
a train traveling at 36 kmph crosses a platform in 30 seconds and a man standing on the platform in 12 seconds . what is the length of the platform in meters ? | "answer distance covered by the train when crossing a man and when crossing a platform when a train crosses a man standing on a platform , the distance covered by the train is equal to the length of the train . however , when the same train crosses a platform , the distance covered by the train is equal to the length o... | a ) 120 meters , b ) 360 meters , c ) 420 meters , d ) 600 meters , e ) can not be determined | a | subtract(multiply(divide(multiply(36, const_1000), const_3600), 30), multiply(divide(multiply(36, const_1000), const_3600), 12)) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)|multiply(n2,#1)|subtract(#2,#3)| | physics |
when positive integer n is divided by positive integer j , the remainder is 14 . if n / j = 134.05 , what is value of j ? | "1 ) we know that decimal part of decimal quotient = { remainder / divisor } so 0.08 , the decimal part of the decimal quotient , must equal the remainder , 14 , divided by the divisor j . 0.05 = 14 / j 0.05 * j = 14 j = 14 / 0.05 = 1400 / 5 = 280 so j = 280 , answer = c ." | a ) 22 , b ) 56 , c ) 280 , d ) 112 , e ) 175 | c | divide(14, subtract(134.05, add(const_100, add(multiply(const_4, const_10), const_2)))) | multiply(const_10,const_4)|add(#0,const_2)|add(#1,const_100)|subtract(n1,#2)|divide(n0,#3)| | general |
what is the sum of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 8 ? | "find the number , upon sum of 3 digits of a number gives a reminder 2 when it is divided by 8 seeing the options after dividing an finding the reminder of 2 my answer was a" | a ) 61,600 , b ) 64,850 , c ) 64,749 , d ) 49,700 , e ) 56,720 | a | multiply(divide(add(divide(subtract(subtract(const_1000, 3), add(add(multiply(multiply(3, 3), const_10), multiply(3, 3)), 3)), 8), const_1), 2), add(subtract(const_1000, 3), add(add(multiply(multiply(3, 3), const_10), multiply(3, 3)), 3))) | multiply(n0,n0)|subtract(const_1000,n0)|multiply(#0,const_10)|add(#2,#0)|add(n0,#3)|add(#4,#1)|subtract(#1,#4)|divide(#6,n2)|add(#7,const_1)|divide(#8,n1)|multiply(#5,#9)| | general |
an engineer undertakes a project to build a road 15 km long in 300 days and employs 35 men for the purpose . after 100 days , he finds only 2.5 km of the road has been completed . find the ( approximate ) number of extra men he must employ to finish the work in time . | "35 workers working already let x be the total men required to finish the task in next 200 days 2.5 km done hence remaining is 12.5 km also , work has to be completed in next 200 days ( 300 - 100 = 200 ) we know that , proportion of men to distance is direct proportion and , proportion of men to days is inverse proport... | a ) a . 43 , b ) b . 53 , c ) c . 55 , d ) d . 68 , e ) e . 60 | b | subtract(divide(multiply(multiply(35, subtract(15, 2.5)), 100), multiply(2.5, subtract(300, 100))), 35) | subtract(n0,n4)|subtract(n1,n3)|multiply(n2,#0)|multiply(n4,#1)|multiply(n3,#2)|divide(#4,#3)|subtract(#5,n2)| | physics |
what least number should be subtracted from 1,439 so that the remainder when divided by 5 , 11 , and 13 will leave in each case the same remainder 3 ? | "the lcm of 5 , 11 , and 13 is 715 . the next multiple is 2 * 715 = 1,430 . 1,430 + { remainder } = 1,430 + 3 = 1,433 , which is 6 less than 1,439 . answer : e ." | a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6 | e | subtract(1,439, add(multiply(multiply(multiply(5, 11), 13), const_2), 3)) | multiply(n1,n2)|multiply(n3,#0)|multiply(#1,const_2)|add(n4,#2)|subtract(n0,#3)| | general |
a and b invests rs . 5000 and rs . 6000 in a business . after 4 months , a withdraws half of his capital and 2 months later , b withdraws one - third of his capital . in what ratio should they share the profits at the end of the year ? | "a : b ( 5000 * 4 ) + ( 2500 * 8 ) : ( 6000 * 6 ) + ( 4000 * 6 ) 40000 : 60000 2 : 3 answer : a" | a ) 2 : 3 , b ) 82 : 31 , c ) 32 : 45 , d ) 34 : 89 , e ) 35 : 21 | a | divide(add(multiply(5000, 4), multiply(divide(6000, const_3), multiply(2, 4))), add(multiply(6000, multiply(2, const_3)), multiply(subtract(6000, divide(6000, const_3)), multiply(2, const_3)))) | divide(n1,const_3)|multiply(n0,n2)|multiply(n3,n2)|multiply(n3,const_3)|multiply(#0,#2)|multiply(n1,#3)|subtract(n1,#0)|add(#1,#4)|multiply(#3,#6)|add(#5,#8)|divide(#7,#9)| | gain |
how long will a boy take to run round a square field of side 20 meters , if he runs at the rate of 12 km / hr ? | "speed = 12 km / hr = 12 * 5 / 18 = 10 / 3 m / sec distance = 20 * 4 = 80 m time taken = 80 * 3 / 10 = 24 sec answer is d" | a ) 52 sec , b ) 45 sec , c ) 60 sec , d ) 24 sec , e ) 39 sec | d | divide(multiply(20, const_4), multiply(12, divide(const_1000, const_3600))) | divide(const_1000,const_3600)|multiply(n0,const_4)|multiply(n1,#0)|divide(#1,#2)| | gain |
( 4300731 ) - ? = 2535618 | "let 4300731 - x = 2535618 then x = 4300731 - 2535618 = 1765113 answer is c" | a ) 1865113 , b ) 1775123 , c ) 1765113 , d ) 1675123 , e ) none of them | c | multiply(4300731, power(add(const_4, const_1), const_4)) | add(const_1,const_4)|power(#0,const_4)|multiply(n0,#1)| | general |
what two - digit number is less than the sum of the square of its digits by 11 and exceeds their doubled product by 4 ? | "let the digits be x and y . the number would be 10 x + y . we are given that 2 xy + 4 = 10 x + y = x ^ 2 y ^ 2 - 11 thus 2 xy + 4 = x ^ 2 + y ^ 2 - 11 x ^ 2 + y ^ 2 - 2 xy = 16 ( x - y ) ^ 2 = 16 ( x - y ) = 4 or - 4 substituting the values of ( x - y ) in the equation 2 xy + 5 = 10 x + y x comes out to be 1 or 9 . . ... | a ) 95 , b ) 99 , c ) 26 , d ) 73 , e ) none of the above | c | add(multiply(const_10, add(subtract(11, 4), const_1)), 4) | subtract(n0,n1)|add(#0,const_1)|multiply(#1,const_10)|add(n1,#2)| | general |
if a solid sphere of radius 10 cms is moulded into 8 spherical solid balls of equal radius , then surface area of each ball ( in sq . cm ) is ? | explanation : 4 / 3 π x 10 x 10 x 10 = 8 x 4 / 3 π rxrxr r = 5 4 π x 5 x 5 = 100 π answer is a | ['a ) 100 π', 'b ) 101 / π', 'c ) 99 π / 12', 'd ) 54 / 13 π', 'e ) 22 / 10 π'] | a | multiply(multiply(power(power(divide(multiply(divide(multiply(multiply(divide(const_4, const_3), power(10, const_3)), const_pi), 8), const_3), multiply(const_4, const_pi)), inverse(const_3)), const_2), const_4), const_pi) | divide(const_4,const_3)|inverse(const_3)|multiply(const_4,const_pi)|power(n0,const_3)|multiply(#0,#3)|multiply(#4,const_pi)|divide(#5,n1)|multiply(#6,const_3)|divide(#7,#2)|power(#8,#1)|power(#9,const_2)|multiply(#10,const_4)|multiply(#11,const_pi) | geometry |
what is the average of 12 , 13 , 14 , 510 , 520 , 530 , 1115 , 1120 , and 1 , 1252140 , 2345 ? | add 12 , 13 , 14 , 510 , 520 , 530 , 1,115 , 1,120 , and 1,125 , 2140 , 2345 grouping numbers together may quicken the addition sum = 9444 4959 / 11 = 858.54 . e | a ) 419 , b ) 551 , c ) 601 , d ) 620 , e ) 858.54 | e | divide(add(add(add(add(add(add(add(add(add(add(12, 13), 14), 510), 520), 530), 1115), 1120), add(1115, const_10)), subtract(2345, add(add(multiply(const_100, const_2), const_4), const_1))), 2345), add(const_10, const_1)) | add(n0,n1)|add(n6,const_10)|add(const_1,const_10)|multiply(const_100,const_2)|add(n2,#0)|add(#3,const_4)|add(n3,#4)|add(#5,const_1)|add(n4,#6)|subtract(n10,#7)|add(n5,#8)|add(n6,#10)|add(n7,#11)|add(#12,#1)|add(#13,#9)|add(n10,#14)|divide(#15,#2) | general |
the price of a certain painting increased by 20 % during the first year and decreased by 25 % during the second year . the price of the painting at the end of the 2 - year period was what percent of the original price ? | "easiest thing to do : assume that price is 100 price at the end of yr 1 : 100 + 20 = 120 price at the end of year 2 = 120 - 120 * 0.25 = 120 * 0.75 = 90 hence required answer = ( 90 / 100 ) * 100 % = 90 % answer is b ." | a ) 102 % , b ) 90 % , c ) 120 % , d ) 85 % , e ) 95 % | b | add(subtract(subtract(20, 25), divide(multiply(25, 20), const_100)), const_100) | multiply(n0,n1)|subtract(n0,n1)|divide(#0,const_100)|subtract(#1,#2)|add(#3,const_100)| | general |
the average age of 15 students of a class is 15 years . out of these , the average age of 5 students is 13 years and that of the other 9 students is 16 years , the age of the 15 th student is | explanation : age of the 15 th student = [ 15 * 15 - ( 13 * 5 + 16 * 9 ) ] = 16 years . answer : b | a ) 11 , b ) 16 , c ) 13 , d ) 14 , e ) 15 | b | subtract(multiply(15, 15), add(multiply(5, 13), multiply(9, 16))) | multiply(n0,n0)|multiply(n2,n3)|multiply(n4,n5)|add(#1,#2)|subtract(#0,#3) | general |
if 64 ( 2 ^ x ) = 1 then x = | "2 ^ x = 1 / 64 2 ^ x = 1 / 2 ^ 6 2 ^ x = 2 ^ - 6 x = - 6 d" | a ) – 2 , b ) – 1 , c ) 0 , d ) - 6 , e ) 5 | d | divide(log(divide(1, 64)), log(2)) | divide(n2,n0)|log(n1)|log(#0)|divide(#2,#1)| | general |
if the charge of staying in a student youth hostel $ 18.00 / day for the first week , and $ 13.00 / day for each additional week , how much does it cost to stay for 23 days ? | "total number of days of stay = 23 charge of staying in first week = 18 * 7 = 126 $ charge of staying for additional days = ( 23 - 7 ) * 13 = 16 * 13 = 208 $ total charge = 126 + 208 = 334 $ answer c" | a ) $ 160 , b ) $ 289 , c ) $ 334 , d ) $ 274 , e ) $ 286 | c | add(multiply(18.00, add(const_3, const_4)), multiply(13.00, subtract(23, add(const_3, const_4)))) | add(const_3,const_4)|multiply(n0,#0)|subtract(n2,#0)|multiply(n1,#2)|add(#1,#3)| | general |
a train passes a station platform in 36 sec and a man standing on the platform in 20 sec . if the speed of the train is 18 km / hr . what is the length of the platform ? | "speed = 18 * 5 / 18 = 5 m / sec . length of the train = 5 * 20 = 100 m . let the length of the platform be x m . then , ( x + 100 ) / 36 = 5 = > x = 80 m . answer : a" | a ) 80 , b ) 240 , c ) 288 , d ) 277 , e ) 221 | a | multiply(20, multiply(18, const_0_2778)) | multiply(n2,const_0_2778)|multiply(n1,#0)| | physics |
if the lcm and hcf of 12 and another number is 60 and 3 respectively . find the other number ? | "hcf x lcm = product of numbers 3 x 60 = 12 x the other number other number = ( 3 x 60 ) / 12 other number = 15 answer : c" | a ) 17 , b ) 12 , c ) 15 , d ) 13 , e ) 11 | c | divide(multiply(60, 3), 12) | multiply(n1,n2)|divide(#0,n0)| | physics |
the perimeter of a triangle is 20 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle | "explanation : area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 20 / 2 = 25 cm 2 answer : option c" | a ) a ) 72 , b ) b ) 828 , c ) c ) 25 , d ) d ) 34 , e ) e ) 35 | c | triangle_area(2.5, 20) | triangle_area(n0,n1)| | geometry |
a reduction in the price of petrol by 10 % enables a motorist to buy 5 gallons more for $ 280 . find the original price of petrol ? | price decreased by 10 % , so 9 / 10 times , which means that original gallons bought increased 10 / 9 times . since this increase equals to 5 gallons then 45 gallons were bought originally ( 45 * 10 / 9 = 50 - - > increase 5 gallons ) . hence original price was 280 / 45 = $ 6.2 answer : e . | a ) $ 11 , b ) $ 5 , c ) $ 45 , d ) $ 400 , e ) $ 6.2 | e | divide(subtract(280, multiply(subtract(const_1, divide(10, const_100)), 280)), subtract(5, divide(const_1, const_2))) | divide(n0,const_100)|divide(const_1,const_2)|subtract(const_1,#0)|subtract(n1,#1)|multiply(n2,#2)|subtract(n2,#4)|divide(#5,#3) | gain |
a train covers a distance of 12 km in 10 minutes . if it takes 6 seconds to pass a telegraph post , then the length of the train is | "explanation : speed = 12 / 10 x 60 km / hr = 72 x 5 / 18 m / sec = 20 m / sec . length of the train = ( speed x time ) = ( 20 x 6 ) m = 120 m answer : option b" | a ) 100 m , b ) 120 m , c ) 140 m , d ) 160 m , e ) 170 cm | b | divide(const_100.0, subtract(divide(const_100.0, 10), 6)) | divide(const_100.0,n1)|subtract(#0,n2)|divide(const_100.0,#1)| | physics |
if x / 2 = y / 4 = z / 6 , then find the value of ( x + y + z ) / z | explanation : x / 2 = y / 4 = z / 6 = k , then x = 2 k , y = 4 k and z = 6 k . now , ( x + y + z ) / z = ( 2 k + 4 k + 6 k ) / 6 k = 12 k / 6 k = 2 answer : option e | a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 6 , d ) 1 / 8 , e ) none of these | e | add(add(const_1, divide(2, 6)), divide(2, const_3)) | divide(n0,n2)|divide(n0,const_3)|add(#0,const_1)|add(#2,#1) | general |
country x taxes each of its citizens an amount equal to 15 percent of the first $ 40000 of income , plus 20 percent of all income in excess of $ 40000 . if a citizen of country x is taxed a total of $ 8000 , what is her income ? | equation is correct , so math must be a problem . 0.15 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 6,000 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 10,000 - - > x = 50,000 . answer : b . | a ) $ 40,000 , b ) $ 50,000 , c ) $ 64,000 , d ) $ 66,667 , e ) $ 80,000 | b | add(divide(subtract(8000, multiply(divide(15, const_100), 40000)), divide(20, const_100)), 40000) | divide(n0,const_100)|divide(n2,const_100)|multiply(n1,#0)|subtract(n4,#2)|divide(#3,#1)|add(n1,#4) | general |
the compound ratio of 2 / 3 , 6 / 7 , 1 / 3 and 1 / 8 is given by ? | "2 / 3 * 6 / 7 * 1 / 3 * 1 / 8 = 1 / 42 answer : b" | a ) 1 / 49 , b ) 1 / 42 , c ) 1 / 09 , d ) 1 / 77 , e ) 1 / 12 | b | inverse(multiply(2, 7)) | multiply(n0,n3)|inverse(#0)| | other |
if w is the set of all the integers between 39 and 99 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ? | "multiples of 2 from 39 to 99 = multiples of 2 from 1 to 99 - multiples of 2 from 1 to 38 = [ 99 / 2 ] - [ 38 / 2 ] = 49 - 19 = 30 multiples of 3 from 39 to 99 = multiples of 3 from 1 to 99 - multiples of 3 from 1 to 38 = [ 99 / 3 ] - [ 38 / 3 ] = 33 - 13 = 20 multiples of 2 and 3 bothi . e . 6 from 39 to 99 = multiple... | a ) 26 , b ) 32 , c ) 33 , d ) 34 , e ) 40 | e | subtract(add(floor(divide(subtract(99, 39), 3)), divide(subtract(99, 39), 2)), floor(divide(subtract(99, 39), multiply(2, 3)))) | multiply(n3,n2)|subtract(n1,n0)|divide(#1,n3)|divide(#1,n2)|divide(#1,#0)|floor(#3)|floor(#4)|add(#2,#5)|subtract(#7,#6)| | other |
the number 500 can be written as the sum of the squares of 2 different positive integers . what is the difference of these 2 integers ? | "22 ^ 2 + 4 ^ 2 = 500 - - > 22 - 4 = 18 . d" | a ) 17 , b ) 16 , c ) 15 , d ) 18 , e ) 13 | d | add(add(add(const_4, 2), add(2, const_2)), 2) | add(n1,const_4)|add(const_2,n1)|add(#0,#1)|add(n1,#2)| | general |
the annual interest rate earned by an investment increased by 10 percent from last year to this year . if the annual interest rate earned by the investment this year was 15 percent , what was the annual interest rate last year ? | "let i = interest rate i ( this year ) = i ( last year ) + 0.1 i ( last year ) = 1.1 i ( last year ) 15 = 1.1 x i ( last year ) i ( last year ) = 15 / 1.1 = 150 / 11 = 13.64 % answer : c" | a ) 14.04 % , b ) 15.04 % , c ) 13.64 % , d ) 12.04 % , e ) 10.04 % | c | divide(multiply(15, const_100), add(15, const_100)) | add(n1,const_100)|multiply(n1,const_100)|divide(#1,#0)| | gain |
a sum of money at simple interest amounts to rs . 845 in 3 years and to rs . 854 in 4 years . the sum is : | "s . i . for 1 year = rs . ( 854 - 815 ) = rs . 39 . s . i . for 3 years = rs . ( 39 x 3 ) = rs . 117 . principal = rs . ( 845 - 117 ) = rs . 728 . answer : option e" | a ) s . 650 , b ) s . 690 , c ) s . 698 , d ) s . 700 , e ) s . 728 | e | subtract(845, divide(multiply(subtract(854, 845), 3), 4)) | subtract(n2,n0)|multiply(n1,#0)|divide(#1,n3)|subtract(n0,#2)| | gain |
find number which is 70 % less than 80 . | "explanation : 70 % less is 30 % of the given number therefore , 30 % of 80 is 24 . answer : c" | a ) 18 , b ) 22 , c ) 24 , d ) 26 , e ) 98 | c | divide(multiply(80, 70), const_100) | multiply(n0,n1)|divide(#0,const_100)| | gain |
the sum of 3 consecutive odd numbers is 20 more than the first of these numbers . what is the middle number ? | solution let the numbers be x , x + 2 , x + 4 then x , ( x + 2 ) + ( x + 4 ) = x + 20 ‹ = › 2 x = 14 ‹ = › x = 7 . therefore middle number = x + 2 = 9 . answer c | a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 10 | c | add(divide(subtract(20, add(const_2, const_4)), subtract(3, const_1)), const_2) | add(const_2,const_4)|subtract(n0,const_1)|subtract(n1,#0)|divide(#2,#1)|add(#3,const_2) | general |
the sum of ages of 4 children born 4 years different each is 48 yrs . what is the age of the elder child ? | "let the ages of children be x , ( x + 4 ) , ( x + 8 ) , ( x + 12 ) years . then , x + ( x + 4 ) + ( x + 8 ) + ( x + 12 ) = 48 4 x = 24 x = 6 x + 12 = 6 + 12 = 18 answer : e" | a ) 8 , b ) 9 , c ) 16 , d ) 17 , e ) 18 | e | divide(add(add(add(add(4, const_4), add(4, const_4)), add(const_4, const_4)), 48), 4) | add(n1,const_4)|add(const_4,const_4)|add(#0,#0)|add(#2,#1)|add(n2,#3)|divide(#4,n0)| | general |
a tank contains 10,000 gallons of a solution that is 7 percent sodium chloride by volume . if 2,500 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ? | "the remaining solution will be approximately what percent sodium chloride ? means : what percent of the remaining solution is sodium chloride . now , since the remaining solution is 10,000 - 2,500 = 7,500 gallons and sodium chloride is 700 gallons ( 7 % of initial solution of 10,000 gallons ) then sodium chloride is 7... | a ) 1.25 % , b ) 3.75 % , c ) 9.33 % , d ) 10.67 % , e ) 11.7 % | c | multiply(divide(multiply(multiply(const_100, const_100), divide(7, const_100)), subtract(multiply(const_100, const_100), add(multiply(add(const_2, const_3), multiply(multiply(add(const_2, const_3), const_2), const_100)), multiply(add(const_2, const_3), const_100)))), const_100) | add(const_2,const_3)|divide(n1,const_100)|multiply(const_100,const_100)|multiply(#1,#2)|multiply(#0,const_2)|multiply(#0,const_100)|multiply(#4,const_100)|multiply(#0,#6)|add(#7,#5)|subtract(#2,#8)|divide(#3,#9)|multiply(#10,const_100)| | gain |
the speed of a boat in still water is 18 kmph . what is the speed of the stream if the boat can cover 48 km downstream or 32 km upstream in the same time ? | "x = the speed of the stream ( 18 + x ) / ( 18 - x ) = 2 / 1 18 + x = 36 - 2 x 3 x = 18 x = 6 km / hour if the speed of the stream is 6 km / hour , then the ' downstream ' speed of the boat is 18 + 6 = 24 km / hour and the ' upstream ' speed of the boat is 18 - 6 = 12 km / hour . in that way , if the boat traveled for ... | a ) 4 kmph , b ) 5 kmph , c ) 6 kmph , d ) 7 kmph , e ) 8 kmph | c | divide(18, add(const_1, const_2)) | add(const_1,const_2)|divide(n0,#0)| | physics |
a train 2000 m long can cross an electric pole in 25 sec and then find the speed of the train ? | "length = speed * time speed = l / t s = 2000 / 25 s = 80 m / sec speed = 80 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 324 kmph answer : b" | a ) 322 , b ) 324 , c ) 326 , d ) 328 , e ) 330 | b | divide(divide(2000, const_1000), divide(25, const_3600)) | divide(n0,const_1000)|divide(n1,const_3600)|divide(#0,#1)| | physics |
a bowl contains equal numbers of red , orange , green , blue , and yellow candies . kaz eats all of the green candies and half of the orange ones . next , he eats half of the remaining pieces of each color . finally , he eats red and yellow candies in equal proportions until the total number of remaining candies of all... | "let x be the original number of each color so there are a total of 5 x candies . kaz eats all of the green candies and half of the orange ones . there are 0 green candies and 0.5 x orange candies remaining . he eats half of the remaining pieces of each color . there are 0.25 x orange candies , and 0.5 x each of red , ... | a ) 27.5 % , b ) 33.3 % , c ) 35.5 % , d ) 42.5 % , e ) 47.5 % | d | multiply(divide(divide(subtract(32, add(divide(divide(const_100, add(const_2, const_3)), const_2), divide(divide(divide(const_100, add(const_2, const_3)), const_2), const_2))), const_2), divide(const_100, add(const_2, const_3))), const_100) | add(const_2,const_3)|divide(const_100,#0)|divide(#1,const_2)|divide(#2,const_2)|add(#2,#3)|subtract(n0,#4)|divide(#5,const_2)|divide(#6,#1)|multiply(#7,const_100)| | general |
the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 61 kg . what is the correct weight ? | "actual total weight is ( 20 x 58.4 - 56 + 61 ) = 1173 kgs actual average weight is 1177 / 20 = 58.65 kgs b" | a ) 58 kgs , b ) 58.65 kgs , c ) 58.95 kgs , d ) 59 kgs , e ) 59.85 kgs | b | divide(add(multiply(58.4, 20), subtract(61, 56)), 20) | multiply(n0,n1)|subtract(n3,n2)|add(#0,#1)|divide(#2,n0)| | general |
n people were sitting on a circular manner , if each of two present in the party except the pairs were adjacent sang a song , if a song lasted for 2 mins and 28 minutes was taken for singing song , find n | each of 2 present in the party = > no . of pairs possible = nc 2 possible adjacent pairs = n total required combinations = nc 2 - n time taken by each combination to sing a song = 2 min total time taken = 2 ( nc 2 - n ) = 28 on solving the above equation , we get n = 14 answer : d | ['a ) 11', 'b ) 12', 'c ) 13', 'd ) 14', 'e ) 15'] | d | divide(28, 2) | divide(n1,n0) | physics |
in the floor of a particular kitchen owned by an abstract artist , each row of tiles to the right of the first row contains two fewer tiles than the row directly to its left . if there are 9 rows in all and a total of 405 tiles in the floor , how many tiles does the leftmost row contain ? | this question can be solved in a variety of ways : with algebra , by testing the answers and by using a great number property shortcut involving consecutive integers . we ' re given a few facts to work with : 1 ) there are 9 rows of tiles . 2 ) when going from ' left to right ' , each row contains two fewer tiles than ... | a ) 53 , b ) 56 , c ) 60 , d ) 64 , e ) 68 | a | subtract(add(divide(405, 9), 9), const_1) | divide(n1,n0)|add(n0,#0)|subtract(#1,const_1) | general |
each of 3 charities in novel grove estates has 8 persons serving on its board of directors . if exactly 4 persons serve on 3 boards each and each pair of charities has 5 persons in common on their boards of directors , then how many distinct persons serve on one or more boards of directors ? a . b . c . d . e . | each group has 8 = 8 + 8 + 8 = 24 max 4 people are in 2 groups , subtract 4 people twice as they are counted twice each pair of groups has 5 in common , so in addition to the 4 people subtract 1 from each group ans : 8 + 8 + 8 - ( 2 ( 4 ) ) - 3 = 13 answer : b | a ) 8 , b ) 13 , c ) 16 , d ) 24 , e ) 27 | b | subtract(subtract(multiply(3, 8), 8), 3) | multiply(n0,n1)|subtract(#0,n1)|subtract(#1,n0) | general |
a mixture of 20 kg of spirit and water contains 10 % water . how much water must be added to this mixture to raise the percentage of water to 25 % | exp . water in the given mixture = 10 * 20 / 100 = 2 kg , and spirit = ( 20 - 2 ) = 18 kg let x kg of water added , then , x + 2 / 20 + x * 100 = = 25 4 x + 8 = 20 + x , or x = 4 kg answer : a | a ) 4 kg , b ) 5 kg , c ) 8 kg , d ) 30 kg , e ) 35 kg | a | divide(subtract(multiply(divide(25, const_100), 20), divide(20, 10)), subtract(const_1, divide(25, const_100))) | divide(n2,const_100)|divide(n0,n1)|multiply(n0,#0)|subtract(const_1,#0)|subtract(#2,#1)|divide(#4,#3) | general |
if rs . 7500 are borrowed at c . i at the rate of 4 % per annum , then after 2 years the amount to be paid is : | "explanation : amount = rs . [ 7500 ( 1 + 4 / 100 ) 2 ] = rs . [ 7500 × 26 / 25 × 26 / 25 ] = rs . 8112 . correct option : d" | a ) rs . 8082 , b ) rs . 7800 , c ) rs . 8100 , d ) rs . 8112 , e ) none | d | multiply(7500, multiply(divide(add(const_100, 4), const_100), divide(add(const_100, 4), const_100))) | add(n1,const_100)|divide(#0,const_100)|multiply(#1,#1)|multiply(n0,#2)| | gain |
a and b invests rs . 10000 each , a investing for 4 months and b investing for all the 12 months in the year . if the total profit at the end of the year is rs . 4000 , find their shares ? | the ratio of their profits a : b = 4 : 12 = 1 : 3 share of a in the total profit = 1 / 4 * 4000 = rs . 1000 share of b in the total profit = 3 / 4 * 4000 = rs . 3000 answer : b | a ) 1000,3500 , b ) 1000,3000 , c ) 1000,2000 , d ) 1000,5000 , e ) 1000,2500 | b | divide(multiply(10000, const_1), const_3) | multiply(n0,const_1)|divide(#0,const_3) | gain |
for all even integers n , h ( n ) is defined to be the sum of the even integers between 2 and n , inclusive . what is the value of h ( 18 ) / h ( 10 ) ? | "mean = median = ( first + last ) / 2 and sum = mean * number of terms h ( 18 ) = [ ( 2 + 18 ) / 2 ] * 9 = 90 h ( 10 ) = ( 2 + 10 ) / 2 ] * 5 = 30 h ( 18 ) / h ( 10 ) = ( 90 ) / ( 30 ) = 3 answer : b" | a ) 1.8 , b ) 3 , c ) 6 , d ) 18 , e ) 60 | b | divide(divide(multiply(add(18, 2), add(divide(subtract(18, 2), const_2), const_1)), const_2), divide(multiply(add(divide(subtract(10, 2), const_2), const_1), add(2, 10)), const_2)) | add(n0,n1)|add(n0,n2)|subtract(n1,n0)|subtract(n2,n0)|divide(#2,const_2)|divide(#3,const_2)|add(#4,const_1)|add(#5,const_1)|multiply(#0,#6)|multiply(#7,#1)|divide(#8,const_2)|divide(#9,const_2)|divide(#10,#11)| | general |
in how many ways can an answer key for a quiz be written if the quiz contains 5 true - false questions followed by 2 multiples - choice questions with 4 answer choices each , if the correct answers to all true - false questions can not be the same ? | there are 2 ^ 5 = 32 possibilities for the true - false answers . however we need to remove two cases for ttttt and fffff . there are 4 * 4 = 16 possibilities for the multiple choice questions . the total number of possibilities is 30 * 16 = 480 . the answer is c . | a ) 160 , b ) 320 , c ) 480 , d ) 600 , e ) 720 | c | multiply(subtract(power(const_2, 5), 2), multiply(4, 4)) | multiply(n2,n2)|power(const_2,n0)|subtract(#1,n1)|multiply(#0,#2) | general |
the difference between simple and compound interest on rs . 1600 for one year at 10 % per annum reckoned half - yearly is ? | "s . i . = ( 1600 * 10 * 1 ) / 100 = rs . 160 c . i . = [ 1600 * ( 1 + 5 / 100 ) 2 - 1600 ] = rs . 164 difference = ( 164 - 160 ) = rs . 4 . answer : d" | a ) 8 , b ) 3 , c ) 9 , d ) 4 , e ) 2 | d | multiply(subtract(power(add(divide(divide(10, const_2), const_100), const_1), const_2), add(divide(10, const_100), const_1)), 1600) | divide(n1,const_2)|divide(n1,const_100)|add(#1,const_1)|divide(#0,const_100)|add(#3,const_1)|power(#4,const_2)|subtract(#5,#2)|multiply(n0,#6)| | gain |
a person travels equal distances with speeds of 4 km / hr , 5 km / hr and 6 km / hr and takes a total time of 47 minutes . the total distance is ? | "let the total distance be 3 x km . then , x / 4 + x / 5 + x / 6 = 47 / 60 37 x / 60 = 47 / 60 = > x = 1.27 total distance = 3 * 1.27 = 3.81 km . answer : b" | a ) 2 km , b ) 4 km , c ) 7 km , d ) 9 km , e ) 5 km | b | multiply(multiply(divide(divide(47, const_60), add(add(divide(const_1, 4), divide(const_1, 5)), divide(const_1, 6))), const_3), const_1000) | divide(n3,const_60)|divide(const_1,n0)|divide(const_1,n1)|divide(const_1,n2)|add(#1,#2)|add(#4,#3)|divide(#0,#5)|multiply(#6,const_3)|multiply(#7,const_1000)| | physics |
one hour after yolanda started walking from x to y , a distance of 10 miles , bob started walking along the same road from y to x . if yolanda ' s walking rate was 3 miles per hour and bob т ' s was 4 miles per hour , how many miles had bob walked when they met ? | "when b started walking y already has covered 3 miles out of 10 , hence the distance at that time between them was 10 - 3 = 7 miles . combined rate of b and y was 3 + 4 = 7 miles per hour , hence they would meet each other in 7 / 7 = 1 hours . in 6 hours b walked 1 * 4 = 4 miles . answer : e ." | a ) 24 , b ) 23 , c ) 22 , d ) 21 , e ) 4 | e | multiply(divide(subtract(10, 3), add(3, 4)), 4) | add(n1,n2)|subtract(n0,n1)|divide(#1,#0)|multiply(n2,#2)| | physics |
a person borrows rs . 5000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 7 % p . a for 2 years . find his gain in the transaction per year . | "explanation : the person borrows rs . 5000 for 2 years at 4 % p . a . simple interest simple interest that he needs to pay = prt / 100 = 5000 × 4 × 2 / 100 = 400 he also lends it at 7 % p . a for 2 years simple interest that he gets = prt / 100 = 5000 × 7 × 2 / 100 = 700 his overall gain in 2 years = rs . 700 - rs . 4... | a ) 167.5 , b ) 150 , c ) 225 , d ) 112.5 , e ) 212.5 | b | divide(subtract(divide(multiply(multiply(5000, 7), 2), const_100), divide(multiply(multiply(5000, 4), 2), const_100)), 2) | multiply(n0,n3)|multiply(n0,n2)|multiply(n1,#0)|multiply(n1,#1)|divide(#2,const_100)|divide(#3,const_100)|subtract(#4,#5)|divide(#6,n1)| | gain |
one fourth of one third of two fifth of a number is 14 . what will be 40 % of that number | "explanation : ( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 14 then x = 14 * 30 = 420 40 % of 420 = 168 answer : option a" | a ) 168 , b ) 150 , c ) 180 , d ) 200 , e ) 250 | a | divide(multiply(divide(14, multiply(multiply(divide(const_1, const_4), divide(const_1, const_3)), divide(const_2, add(const_2, const_3)))), 40), const_100) | add(const_2,const_3)|divide(const_1,const_4)|divide(const_1,const_3)|divide(const_2,#0)|multiply(#1,#2)|multiply(#3,#4)|divide(n0,#5)|multiply(n1,#6)|divide(#7,const_100)| | gain |
a vantakes 6 hours to cover a distance of 540 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ? | time = 6 distence = 540 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 540 / 9 = 60 kmph a ) | a ) 60 kmph , b ) 61 kmph , c ) 62 kmph , d ) 64 kmph , e ) 66 kmph | a | divide(540, multiply(divide(3, 2), 6)) | divide(n2,n3)|multiply(n0,#0)|divide(n1,#1) | physics |
a certain fruit stand sold apples for $ 0.80 each and bananas for $ 0.70 each . if a customer purchased both apples and bananas from the stand for a total of $ 7.30 , what total number of apples and bananas did the customer purchase ? | "let ' s start with 1 apple for $ 0.80 . let ' s subtract $ 0.80 from $ 7.30 until we get a multiple of $ 0.70 . $ 7.30 , $ 6.50 , $ 5.70 , $ 4.90 = 7 * $ 0.70 the customer purchased 7 bananas and 3 apples . the answer is b ." | a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13 | b | add(divide(subtract(7.30, multiply(0.80, const_2)), 0.70), const_2) | multiply(n0,const_2)|subtract(n2,#0)|divide(#1,n1)|add(#2,const_2)| | other |
a can do a piece of work in 4 days . b can do it in 9 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ? | "c = 1 / 2 - 1 / 4 - 1 / 9 = 5 / 36 = > 36 / 5 days answer : b" | a ) 22 days , b ) 36 / 5 days , c ) 67 days , d ) 17 / 7 days , e ) 18 days | b | divide(multiply(4, 9), divide(subtract(multiply(4, 9), multiply(add(divide(multiply(4, 9), 4), divide(multiply(4, 9), 9)), 2)), 2)) | multiply(n0,n1)|divide(#0,n0)|divide(#0,n1)|add(#1,#2)|multiply(n2,#3)|subtract(#0,#4)|divide(#5,n2)|divide(#0,#6)| | physics |
a number when divided by a certain divisor left remainder 255 , when twice the number was divided by the same divisor , the remainder was 112 . find the divisor ? | easy solution : n = dq 1 + 255 2 n = 2 dq 1 + 51 0 - ( 1 ) 2 n = dq 2 + 112 - ( 2 ) as ( 1 ) = ( 2 ) = 2 n d * ( q 2 - 2 q 1 ) = 398 d * some integer = 398 checking all options only ( c ) syncs with it . answer c | a ) 370 , b ) 365 , c ) 398 , d ) 456 , e ) 460 | c | subtract(multiply(255, const_2), 112) | multiply(n0,const_2)|subtract(#0,n1) | general |
if 30 % of a number is 12.6 , find the number ? | "a 40" | a ) 42 , b ) 40 , c ) 26 , d ) 36 , e ) 66 | a | divide(divide(12.6, const_100), divide(30, const_100)) | divide(n1,const_100)|divide(n0,const_100)|divide(#0,#1)| | gain |
5 + 3 | a | a ) 8 , b ) 13 , c ) 28 , d ) 6 , e ) 2 | a | multiply(divide(5, 3), const_100) | divide(n0,n1)|multiply(#0,const_100)| | general |
find the number , difference between number and its 3 / 5 is 60 . | "explanation : let the number = x , then , x - ( 3 / 5 ) x = 60 , = > ( 2 / 5 ) x = 60 = > 2 x = 60 * 5 , = > x = 150 answer : option a" | a ) 150 , b ) 153 , c ) 154 , d ) 155 , e ) 156 | a | multiply(divide(60, const_2), 5) | divide(n2,const_2)|multiply(n1,#0)| | general |
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